id:A112505 - OEIS Search Results

Search: id:A112505

Displaying 1-1 of 1 results found.

page 1

Number of primitive prime factors of 10^n-1.

+0
7

1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 3, 1, 2, 2, 2, 2, 1, 2, 3, 3, 1, 1, 3, 2, 2, 3, 5, 3, 3, 5, 2, 3, 3, 1, 3, 1, 1, 2, 4, 3, 4, 3, 2, 4, 2, 1, 2, 3, 4, 2, 4, 2, 4, 2, 3, 2, 2, 3, 7, 1, 5, 4, 2, 2, 3, 3, 3, 2, 2, 3, 3, 3, 3, 2, 4, 4, 6, 2, 5, 2, 3, 2, 3, 3, 3, 2, 5, 3, 7, 3, 1, 3, 5, 4, 3, 2, 4, 4 (list; graph; listen)

	OFFSET	`1,5`
	COMMENT	`Also the number of primes whose reciprocal is a repeating decimal of length n. The number of numbers in each row of table A046107. By Zsigmondy's theorem, a(n) >= 1. When a(n)=1, the corresponding prime is called a unique prime (see A007498, A040017 and A051627).`
	LINKS	`Eric Weisstein's World of Mathematics, Primitive Prime Factor` `Eric Weisstein's World of Mathematics, Zsigmondy Theorem` `Eric Weisstein's World of Mathematics, Unique Prime`
	MATHEMATICA	`pp={}; Table[f=Transpose[FactorInteger[10^n-1]][[1]]; p=Complement[f, pp]; pp=Union[pp, p]; Length[p], {n, 66}]`
	CROSSREFS	`Cf. A007138 (smallest primitive prime factor of 10^n-1), A102347 (number of distinct prime factors of 10^n-1).` `Sequence in context: A037805 A106825 A156608 this_sequence A104638 A057155 A037812` `Adjacent sequences: A112502 A112503 A112504 this_sequence A112506 A112507 A112508`
	KEYWORD	`hard,nonn`
	AUTHOR	`T. D. Noe (noe(AT)sspectra.com), Sep 08 2005`

page 1

Search completed in 0.002 seconds

Last modified December 16 17:18 EST 2009. Contains 170825 sequences.

AT&T Labs Research